Many-body wave scattering problems in the case of small scatterers

Scattering of electromagnetic (EM) waves by many small impedance particles (bodies), embedded in a homogeneous medium, is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the effective EM field in the limiting medium, in the limit a → 0, where a is the characteristic size of a particle and the number M (a) of the particles tends to infinity at a suitable rate. The proposed theory allows one to create a medium with a desirable spatially inhomogeneous permeability. The main new physical result is the explicit analytical formula for the permeability µ(x) of the limiting medium. The computational results confirm a possibility to create the media with various distributions of µ(x).

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“…It has led to a recipe for creating materials with a desired refraction coefficient in [19], [20]. [21].…”

Section: Introductionmentioning

confidence: 99%

Application of the asymptotic solution to EM field scattering problem for creation of media with prescribed permeability

Ramm

Andriychuk

2013

J. Appl. Math. Comput.

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“…The functions σ m are unknown and should be found from the boundary conditions (5). Equation ( 4) is satisfied by U of the form (8) with arbitrary continuous σ m . To satisfy the boundary condition (5) one has to solve the following equation obtained from the boundary condition (5):…”

Section: Introduction and Resultsmentioning

confidence: 99%

Heat Transfer in a Complex Medium

Ramm

2016

Understanding Complex Systems

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The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting field is derived when the characteristic size a of the small bodies tends to zero, their total number N (a) tends to infinity at a suitable rate, and the distance d = d(a) between neighboring small bodies tends to zero: a << d, lima→0 a d(a) = 0. No periodicity is assumed about the distribution of the small bodies. These results are basic for a method of creating a medium in which heat signals are transmitted along a given line. The technical part for this method is based on an inverse problem of finding potential with prescribed eigenvalues.

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“…The methods developed in this paper were applied to acoustic problems in [11], to heat transfer in the medium where many small bodies are distributed in [13], to wave scattering by many nano-wires in [14]. In Section 2 the theory of EM wave scattering is developed for small perfectly conducting bodies (particles) of arbitrary shapes.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scattering of electromagnetic waves by many small perfectly conducting or impedance bodies

Ramm

2015

Journal of Mathematical Physics

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A theory of electromagnetic (EM) wave scattering by many small particles of an arbitrary shape is developed. The particles are perfectly conducting or impedance. For a small impedance particle of an arbitrary shape, an explicit analytical formula is derived for the scattering amplitude. The formula holds as a → 0, where a is a characteristic size of the small particle and the wavelength is arbitrary but fixed. The scattering amplitude for a small impedance particle is shown to be proportional to a 2−κ , where κ ∈ [0, 1) is a parameter which can be chosen by an experimenter as he/she wants. The boundary impedance of a small particle is assumed to be of the form ζ = ha −κ , where h = const, Reh ≥ 0. The scattering amplitude for a small perfectly conducting particle is proportional to a 3 , and it is much smaller than that for the small impedance particle. The many-body scattering problem is solved under the physical assumptions a ≪ d ≪ λ, where d is the minimal distance between neighboring particles and λ is the wavelength. The distribution law for the small impedance particles isHere, N(x) ≥ 0 is an arbitrary continuous function that can be chosen by the experimenter and N (∆) is the number of particles in an arbitrary sub-domain ∆. It is proved that the EM field in the medium where many small particles, impedance or perfectly conducting, are distributed, has a limit, as a → 0 and a differential equation is derived for the limiting field. On this basis, a recipe is given for creating materials with a desired refraction coefficient by embedding many small impedance particles into a given material. C 2015 AIP Publishing LLC. [http://dx

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Many-body wave scattering problems in the case of small scatterers

Cited by 11 publications

References 30 publications

Application of the asymptotic solution to EM field scattering problem for creation of media with prescribed permeability

Application of the asymptotic solution to EM field scattering problem for creation of media with prescribed permeability

Heat Transfer in a Complex Medium

Scattering of electromagnetic waves by many small perfectly conducting or impedance bodies

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